The evolution variational inequality for weighted Wasserstein metrics holds on non-convex bounded domains by absorbing boundary integrals via Sobolev trace embeddings and a variant of Kato's inequality.
Mimura, The variational formulation of the fully parabolic Keller--Segel system with degenerate diffusion
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The evolution variational inequality for weighted Wasserstein metrics in non-convex bounded domains
The evolution variational inequality for weighted Wasserstein metrics holds on non-convex bounded domains by absorbing boundary integrals via Sobolev trace embeddings and a variant of Kato's inequality.